To find the area of a triangle given its vertices, we can use the formula:
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the triangle's vertices.
Given the vertices of the triangle:
- \(A(0, 3)\)
- \(B(10, 6)\)
- \(C(6, 3)\)
Substituting these coordinates into the formula:
\[ \text{Area} = \frac{1}{2} \left| 0(6-3) + 10(3-3) + 6(3-6) \right| \]
Calculating each term:
\[ = \frac{1}{2} \left| 0 + 10 \cdot 0 + 6(-3) \right| \] \[ = \frac{1}{2} \left| 0 + 0 - 18 \right| \] \[ = \frac{1}{2} \left| -18 \right| \] \[ = \frac{1}{2} \cdot 18 = 9 \]
Thus, the area of the triangle is \(9\) square units.
Therefore, the answer is \(9\).
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